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This work studies the Generalized Singular Value Thresholding (GSVT) operator Prox σ g (·), Prox σ g (B) = arg min X m i=1 g(σi(X)) + 1 2 ||X − B|| 2 F , associated with a nonconvex function g defined on the singular values of X. We prove that GSVT can be obtained by performing the proximal operator of g (denoted as Proxg(·)) on the singular values since(More)
In this paper, we present theoretical analysis of SON – a convex optimization procedure for clustering using a sum-of-norms (SON) regularization recently proposed in [8, 10, 11, 17]. In particular, we show if the samples are drawn from two cubes, each being one cluster, then SON can provably identify the cluster membership provided that the distance between(More)
The effects of supplementation with the benthic diatom Cylindrotheca fusiformis on the growth of the sea cucumber Apostichopus japonicus and water quality was studied in six sea cucumber culturing ponds (600 m2 each) from November 2011 to November 2012. The nutrients for sea cucumbers in the control group were supplied solely by the spring tide inflow;(More)
In the following development, we consider the following problem Prox g (b) = arg min x≥0 f b (x) = g(x) + 1 2 (x − b) 2 , (1) where g(x) satisfies the following assumption. Set C b (x) = b − x and D(x) = ∇g(x). Let ¯ b = sup{b | C b (x) and D(x) have no intersection}, and x ¯ b 2 = inf{ x | (x, y) is the intersection point of C¯ b (x) and D(x)}. 1.1 Proof(More)
In many problems in machine learning and operations research, we need to optimize a function whose input is a random variable or a probability density function, i.e. to solve optimization problems in an infinite dimensional space. On the other hand, online learning has the advantage of dealing with streaming examples, and better model a changing(More)
With the success of modern internet based platform , such as Amazon Mechanical Turk, it is now normal to collect a large number of hand labeled samples from non-experts. The Dawid-Skene algorithm, which is based on Expectation-Maximization update, has been widely used for inferring the true labels from noisy crowdsourced labels. However, Dawid-Skene scheme(More)
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